Question

A can do a piece of work in
4 days. B and C together
do it in 3 days. While
A and C together can do it
in 2 days, How long B alone
would take to do the whole work?​

Answer 1

Answer:

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Step-by-step explanation:

Amount of work A does in 1 h = (1/4) <= A takes 4 h to complete a piece of work.

Amt of work B and C can complete in 1 h = (1/3) <= B and C take 3 h to complete a piece of work.

Amt of work A and C can complete in 1 h = (1/2) <= A and C take 2 h to complete a piece of work.

Rewriting as equations : A + C = 1/2, B + C = 1/3, A = 1/4

A + C = 1/2 => 1/4 + C = 1/2 => C = 1/2 - 1/4 = 1/4 ie C takes 4 h to complete a piece of work.

B + C = 1/3 => B + 1/4 = 1/3 => B = 1/3 - 1/4 = 1/12 ie B takes 12 h to complete a piece of work.

OR

A + C = 1/2, B + C = 1/3 => (A + C) - (B + C) = 1/2 - 1/3

A - B = 1/2 - 1/3 = 1/6

1/4 - B = 1/6

B = 1/4 - 1/6 = 1/12 ie B takes 12 h to complete a piece of work.